STAT230 Study Guide - Final Guide: Joint Probability Distribution, Probability Distribution, Independent And Identically Distributed Random Variables

• School: University of Waterloo
• Department: Statistics
• Course: STAT230
• Professor: phdstudent

Document Summary

Definitions: the expected value of a function of discrete rv"s x and y, g(x, y) is: This can be extended beyond two variables x and y: property of multivariate expectation, variance: some forms are easier to compute than others, the covariance of x and y, denoted [( )( )] If x and y are independent, then cov(x, y) = 0. The converse is not true: suppose x and y are independent random variables. Then, if and are any two functions, [ ] [ ] [ ]: the correlation coefficient of x and y is. Note: this is a measure of the strength of the relationship between x and y. lies in the interval [-1,1]: properties of covariance: Intuition: think of this as multiplying the two terms (ax+by) and (cu+dv) together. (which is exactly how it is derived using the definition: variance of a linear combination: In fact, more generally if we have n r. v"s x1,x2, ,xn.